Q. If $a + b = 8,$ then $ab$ is greater when
A) $a = 4,\ b = 4$
B) $a = 3,b = 5$
C) $a = 6,b = 2$
D) None of these
Explanation
(a)
We know that,
$AM \geq GM$
$\Rightarrow \frac{a + b}{2} \geq \sqrt{ab}$
$\Rightarrow 4 \geq \sqrt{ab}\ \ \ \ (\because a + b = 8$ given)
$\Rightarrow ab \leq 16$
Equality holds when number are equal. So, $ab$ is equal to 16 when $a = 4,b = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.